Leak Simulaton Of Network Based On The Theory Of Slow Transient Flow

Leak of urban water supply network not only wastes large water, causes economic loss, but also affects the normal operation of the city. So it is paid more and more attention. It is difficult for leak diagnosis and localization as a result of the complex topology and most of water supply network being buried. This paper based on slowly transient theory and using the method of system identification, establishes the leak model of pipe network to make a theoretical study.The complex large pipe network can be expressed to simple and intuitive "network map" by graph theory to simplify the hydraulic calculation. According to Bernoulli Equation of unsteady flow, the hydraulic calculation model of multi-source pipe network based on graph theory in slowly transient state is established, which can provide more information of hydraulic elements in slowly transient state. When the leakage accident conditions of pipe network is simulated, assuming that the leakage occurs in the node or nearby node , the leakage discharge is regard as a part of the node discharge, the extent of leakage is expressed with the leakage area, and leak discharge is calculated through the orifice flow formula. On the basis of leak model based on slowly transient flow, this paper, using matrix theory, derives the analytical expressions and gets the discrete solution. A simple example network is carried on the hydraulic simulation calculation of the model.Leakage of pipe network will be inevitable to change the running state of network that is they have close contact with each other. According to this relationship, this paper establishes the leak simulation model based on least square principle and the leak simulation model based on Bayes theory, derives the objective function on the slowly transient state parameters, and determines the corresponding constraints, so that the leak simulation problem of slowly transient network is changed into a optimal problem of nonlinear function by mathematical method to solve.For the actual pipe network, we hope that the monitoring points are as less as possible, but have strong representative to reflect the actual running state of pipe network. So the optimal layout of the monitoring points is necessary. According to the FCM algorithm of fuzzy clustering analysis, the method of optimal layout to flow and pressure monitoring points of water supply network based on reflecting the leak is proposed. Through analyze the example network, the specific process of the optimal layout to the monitoring points of flow and pressure is given.Finally, according to above method, the leakage simulation program of the pipe network based on slowly transient flow is compiled, the leakage conditions in three different schemes are solved, and the detection results of two models are analyzed. The simulation results show that, by comparing the deviation and probability of flow and pressure in different schemes with the given threshold, the leakage region can be roughly determined, and the leak location is further defined, which can reach high detection accuracy.